The main interest of this theorem is in classifying the indefinite orthogonal groups, which in turn is fundamental because the Lorentz group is an indefinite orthogonal groups, see: all indefinite orthogonal groups of matrices of equal metric signature are isomorphic.
It also tells us that a change of basis does not the alter the metric signature of a bilinear form, see matrix congruence can be seen as the change of basis of a bilinear form.
The theorem states that the number of 0, 1 and -1 in the metric signature is the same for two symmetric matrices that are congruent matrices.
For example, consider:
The eigenvalues of are and , and the associated eigenvectors are:symPy code:and from the eigendecomposition of a real symmetric matrix we know that:
A = Matrix([[2, sqrt(2)], [sqrt(2), 3]])
A.eigenvects()Now, instead of , we could use , where is an arbitrary diagonal matrix of type:With this, would reach a new matrix :Therefore, with this congruence, we are able to multiply the eigenvalues of by any positive number and . Since we are multiplying by two arbitrary positive numbers, we cannot change the signs of the original eigenvalues, and so the metric signature is maintained, but respecting that any value can be reached.
Note that the matrix congruence relation looks a bit like the eigendecomposition of a matrix:but note that does not have to contain eigenvalues, unlike the eigendecomposition of a matrix. This is because here is not fixed to having eigenvectors in its columns.
But because the matrix is symmetric however, we could always choose to actually diagonalize as mentioned at eigendecomposition of a real symmetric matrix. Therefore, the metric signature can be seen directly from eigenvalues.
What this does represent, is a general change of basis that maintains the matrix a symmetric matrix.
"De novo" means "starting from scratch", that is: you type the desired sequence into a computer, and the synthesize it.
The "de novo" part is important, because it distinguishes this from the already well solved problem of duplicating DNA from an existing DNA template, which is what all our cells do daily, and which can already be done very efficiently in vitro with polymerase chain reaction.
Notably, the dream of most of those companies is to have a machine that sits on a lab bench, which synthesises whatever you want.
The initial main applications are likely going to be:but the real pipe dream is building and bootstraping entire artificial chromosomes
- polymerase chain reaction primers (determine which region will be amplified
- creating a custom sequence to be inserted in a plasmid, i.e. artificial gene synthesis
News coverage:
- 2023-03 twitter.com/sethbannon/status/1633848116154880001
- 2020-10-05 www.nature.com/articles/s41587-020-0695-9 "Enzymatic DNA synthesis enters new phase"
Nuclera eDNA enzymatic de novo DNA synthesis explanatory animation (2021)
Source. The video shows nicely how Nuclera's enzymatic DNA synthesis works:- they provide blocked nucleotides of a single type
- add them with the enzyme. They use a werid DNA polymerase called terminal deoxynucleotidyl transferase that adds a base at a time to a single stranded DNA strand rather than copying from a template
- wash everything
- do deblocking reaction
- and then repeat until done
Marc Verdiell is a French electrical engineer born in 1963 or 1964[ref] and best known for being the creator and host of the CuriousMarc YouTube channel where he does mind blowing repairs and reverse engineering of vintage computers and other electronic equipment.
Marc sold his company LightLogic, an optoelectronics company he founded, to Intel in April 2001. This was just after the dot-com crash, but Intel apparently still correctly believed that the networking and the Internet would continue to grow and was investing in the area. His associate Frank Shum sued claiming he should be credited for some of the inventions sold but lost and Marc got it all.[ref][ref][ref]. Marc was then almost immediately appointed an Intel fellow at the extremelly early age of 37, and then stayed for a few years at Intel until 2006 according to his LinkedIn.[ref][ref]
Marc Verdiell at the Computer History Museum
. Source. Location inferred from Marc's videos, but likely, he often frequents the place, and it looks a bit like that.Marc's full name is actualy Jean-Marc Verdiell, but Ciro Santilli remembers there was one YouTube video where he mentions he gave up on "Jean" partly because anglophones would murder its pronounciation all the time.
Marc's PhD thesis is listed at: theses.fr/1990PA112048 and it is entitled:which is translated into English as:but the full text is not available online.
Phase locking of semiconductor laser arrays
Profile of Marc Verdiell by Gizmodo (2018)
Source. And a person who makes open educational content like Marc, truly deserves it.
Atherton managed to keep the entire place green and every house has a pool. Wikipedia comments web.archive.org/web/20220906010554/https://www.forbes.com/home-improvement/features/most-expensive-zip-codes-us/:
Atherton is known for its wealth; in 1990 and 2019, Atherton was ranked as having the highest per capita income among U.S. towns with a population between 2,500 and 9,999, and it is regularly ranked as the most expensive ZIP Code in the United States [(94027)]. The town has very restricting zoning, only permitting one single-family home per acre and no sidewalks. The inhabitants have strongly opposed proposals to permit more housing construction and Forbes confirms it for 2022: web.archive.org/web/20220906010554/https://www.forbes.com/home-improvement/features/most-expensive-zip-codes-us/, by far on top.
Generate public private key, test encrypt and test decrypt:
# Create your pubkey.
gpg --gen-key
gpg --armor --output pubkey.gpg --export <myemail>
# Encrypt using someone's pubkey.
gpg --import pubkey2.gpg
echo 'hello world' > hello.txt
gpg --output hello.txt.gpg --encrypt --recipient <other-email> hello.txt
# Double check it is not plaintext in the encrypted message.
grep hello hello.txt.gpg
# Decrypt.
gpg --output hello.decrypt.txt --decrypt --recipient <myemail> hello.txt.gpg
diff -u hello.decrypt.txt hello.txt Unlisted articles are being shown, click here to show only listed articles.